Holography is used in a variety of applications ranging from printed holograms used on credit cards to metrology devices used in integrated circuit manufacturing. Traditional holography methods involve the recording on film of phase shifts of the object of interest. These phase shifts are recorded using two beams of coherent light, an object beam, which impinges upon the object of interest, and a reference beam. The interference of the object beam and the reference beam generates phase patterns, which correlate to physical feature of the object of interest. Once the image is recorded, an image of the original object can be regenerated by passing light through the recording film providing a three dimensional holographic image. A traditional photograph records the intensity of light reaching a piece of film. A lens is used to record the image of an object so that each point on the object is focused to a point on the film. The film records the intensities at each point and we recognize this as the original object. A hologram is different because it is capable of recording phase. Since light is a wave, it has the ability to interfere with itself. Through this interference we can find the phase of the light. A hologram is made by taking a very coherent light source and splitting it into two beams. One beam goes straight to the film. This beam provides a reference of what the laser light looks like and is called the reference beam. The other beam illuminates the object and is called the object beam. When this light hits the object, it is reflected off toward the film. At the film, interference occurs between the electric fields of the reference beam and the object beam. If the angle between the reference beam and the object beam is near zero it is called an xe2x80x9con-axis hologramxe2x80x9d. If the angle is greater than zero it is called an xe2x80x9coff-axis hologramxe2x80x9d. In both situations the intensity of the interference is recorded by the film. This is described by Equations 2.1 and 2.2.
H is the intensity field recorded onto the film, O is the object beam""s electric field, and R is the electric field due to the reference beam. Unlike a traditional photograph, in holography, what gets recorded onto the film does not look like the object. The |O|2 term is the intensity pattern of the light that came from the object and |R|2 is the intensity of the reference beam. O*R and OR* are the interference terms and is what we are interested in. To view the hologram the reference beam must be shined onto the film. The virtual image appears at the same location as the original object. The virtual image has depth and can be viewed from different angles just as the original could. A real image is also formed and can be projected onto a white card.
The advent of the charged coupled device (CCD) and digital cameras allows the application of digital technology to the field of holography, eliminating the need for film recordings. Digital holograms offer some advantages over prior art film recordings. Reconstruction of the image is carried out using software thereby permitting more control over the reconstructed image and time and cost of the hologram are reduced. However, the prior art digital holograms suffer from what is referred to as the 2xcfx80 ambiguity problem. Since the recording only records a phase shift in a wave, features of the target object greater than one wavelength are not recorded properly. The phase imaging by digital holography allows sub-wavelength resolution in microscopic imaging. However for axial ranges greater than one wavelength the phase image has 2xcfx80 ambiguity and is therefore unable to distinguish points that are separated by an axial distance that is a multiple of the wavelength. Depending upon the application involved, a wavelength is selected which is sufficiently long to cover the range required to avoid 2xcfx80 ambiguity. However, the longer the wavelength, the lower the resolution.
Phase unwrapping is known in the art as a method to resolve 2xcfx80-ambiguity. The simplest form of phase unwrapping is to move along the phase map until you get to a sudden 2xcfx80 discontinuity. The program can identify this sudden jump and add xcex to the height of the map to compensate for the expected discontinuity. At the next discontinuity, the program adds 2xcex to the height map, and so on.
Another phase unwrapping method known in the art is the minimum spanning tree method. The minimum spanning tree method is an attempt to prevent spike noise and local inconsistencies from reducing the accuracy of the overall unwrapped image. The first step of this method is to go from one pixel to its nearest neighbor with the smallest change in phase. When each pixel is being considered, neighboring pixels are looked at and used to try to suppress noise spikes. In the next step, tiles of pixels are made. The tiles are designed to slightly overlap. The edges are used to compare each tile to its neighbor. Areas where there are inconsistencies are avoided so that their errors do not continue for the rest of the map.
All forms of phase unwrapping algorithms make the assumption that the surface does not have discontinuities more than 2xcfx80. If the surface violates this then the map will not be accurate. This is a problem for maps that are not well behaved or that have speckle that must first be removed.
It is known in the art that contours can be generated by using two different wavelengths to produce a hologram. This procedure is similar to that of a regular hologram. The difference being that, after the film is exposed to the object beam and reference beam, it is exposed again with an object beam and a reference beam of a slightly different wavelength. The closer together the frequency the further apart the contours are spaced.
It is known in the art to use digital holography to assign accurate, consistent intensity values to an image and to make it possible to calculate and extrapolate phase information. The field of digital holography is relatively new because, until recently, the needed devices such as a CCD (charge-coupled device) and computers have not been capable of this task.
There remains a need for a system and method to provide a high-resolution hologram for objects with surface discontinuities greater than 2xcfx80 that eliminates 2xcfx80 ambiguity.
However, in view of the prior art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill in the pertinent art how the identified need could be fulfilled.
The method in accordance with the present invention resolves the 2xcfx80-ambiguity associated with an axial range greater than one wavelength by a method that employs digital holograms generated with two or more wavelengths.
The method in accordance with the present invention is a combination of digital holographic phase mapping and contour generation. The contour generation is used to determine what fringe number a pixel is on, and the phase map is then used to produce sub-wavelength resolution. This makes it possible to get detailed sub-wavelength resolution over several wavelengths of range without the using phase unwrapping algorithms.
Additionally, since the two-wavelength method of the present invention still has ambiguities, they are just separated by a much larger distance; conventional phase unwrapping methods are still applicable. If the assumption that the surface does not have discontinuities greater than xcex is reasonable, then the assumption that the surface does not have discontinuities greater then 10xcex is reasonable.
In accordance with the present invention, a digital holographic phase-imaging method to resolve ambiguities includes generating a digital holographic phase map of an object at a first wavelength, generating a digital holographic phase map of the object at a second wavelength, subtracting the second phase map from the first phase map, resolving the fringe number for each pixel phase value, and referencing the digital holographic phase map at the first wavelength thereby reproducing the image of the object. It is also within the scope of the present invention to employ the method of the present invention utilizing more than two wavelengths.
In an embodiment of the present invention, the step of generating a digital holographic phase map of an object at a first wavelength, includes recording a first digital hologram image of the object at the first wavelength utilizing an object beam and a reference beam, recording a first digital object image of the object at the first wavelength utilizing an object beam, recording a first digital reference image of the object at the first wavelength utilizing a reference beam, and subtracting an intensity pattern of the first digital object image and an intensity pattern of the first digital reference image from the first digital hologram image resulting in a digital holographic phase map of the object at the first wavelength. And, recording a second digital hologram image of the object at the second wavelength utilizing an object beam and a reference beam, recording a second digital object image of the object at the second wavelength utilizing an object beam, recording a second digital reference image of the object at the second wavelength utilizing a reference beam, subtracting an intensity pattern of the second digital object image and an intensity pattern of the second digital reference image from the second digital hologram image resulting in the digital holographic phase map of the object at the second wavelength.
In a specific embodiment, the angle between the reference beam and the object beam at the first and second wavelengths is greater than zero, thereby producing an off-axis hologram. Additionally, the first wavelength and the second wavelength can be within the visible range or the infrared range, while additional wavelengths are within the scope of the invention.
The referencing the digital holographic phase map at the first wavelength, thereby reproducing the image of the object as presented by the present invention, includes simulating a reference wave at a first wavelength incident upon the digital holographic phase map.
Additionally, resolving the fringe number for each pixel phase value includes converting the result of the subtracting step into a plurality of distance values, dividing each distance value by the second wavelength, truncating the result of the dividing step, multiplying the result of the truncating step by the second wavelength, resulting in the closest integer wavelength for each pixel value, and adding the high resolution distance value to the closest integer wavelength for each pixel value. At this point, the method includes adding xcfx80 to the closest integer wavelength for each pixel value when the closest integer wavelength value is xcfx80/2 greater than the distance value, and subtracting xcfx80 from the closest integer wavelength for each pixel value when the closest integer wavelength value is xcfx80/2 less than the distance value.
In an additional embodiment of the present invention, a method is provide for recording a first hologram image at a first wavelength, recording an first object image at a first wavelength, recording a first reference image at a first wavelength, generating a first phase map at a first wavelength from the recorded first hologram image, first object image and first reference image, recording a second hologram image at a second wavelength, the second wavelength longer than the first wavelength, recording a second object image at a second wavelength, recording a second reference image at a second wavelength, generating a second phase map at a second wavelength from the recorded second hologram image, second object image and second reference image, subtracting the second phase map from the first phase map, resolving the fringe number for each pixel phase value, referencing the digital holographic phase map at the first wavelength, calculating a topographical map of the object.
In accordance with the present invention, a digital holographic phase-imaging system is provided, to include a digital holographic imager to provide a first hologram image, a first object image and a first reference image at a first wavelength and a second hologram image, a second object image and a second reference image at a second wavelength, a phase map generator to receive the first hologram image, the first object image, the first reference image, the second hologram image, the second object image and the second reference image and to generate a first phase map comprising a plurality of pixels at a first wavelength and a second phase map comprising a plurality of pixels at a second wavelength, a contour generator to determine the fringe number of the plurality of pixels of the plurality of phase maps, and a resolution generator to produce sub-wavelength resolution of the object image.
The digital holographic imager of the present invention further including a first laser source to illuminate a reference mirror and a target object to generate the first hologram image, the first object image and the first reference image at the first wavelength, a second laser source to illuminate a reference mirror and a target object to generate the second hologram image, the second object image and the second reference image at the second wavelength, and an image capture and storage device to transmit the first hologram image, the first object image, the first reference image, the second hologram image, the second reference image and the second object image to the phase map generator.
In accordance with the present invention, multiple phase maps are generated through the use of digital holography and analyzed using a software program. By using two different wavelengths to generate phase maps, the 2xcfx80 ambiguity can be resolved without the use of phase unwrapping algorithms.
In a specific embodiment of the present invention, a method of holography using a Michelson interferometer with the reference mirror tilted off axis is provided. The hologram is recorded using a monochromatic digital camera. Through the use of Huygens"" wavelet principle and fast Fourier transforms the original object is reproduced not only in intensity but also in phase. It is the reproduction of the phase maps that allows the topographical contours to be generated.
Once the phase maps have been obtained using digital holography, the two-phase maps are subtracted from each other giving a beat wavelength. The beat wavelength will be longer and can be used to resolve the fringe number that a pixel""s phase value is on, resolving the 2xcfx80 ambiguities. The shortest wavelength phase map is then referenced to generate high, sub-wavelength resolution. In this way, a topographic map can be produced which has a resolution of 10 nm over several wavelengths with no ambiguities.